Water Journal : Water Journal May 2011
refereed paper demand management water MAY 2011 65 Normally, the more the people in the house, the less the per-person consumption, therefore, α is less than or equal to 1. For each lot size cluster, it is assumed that the outdoor consumption is constant, so the total consumption can be expressed as Q = Qi+kHα (2) where Qi is the combination of the outdoor consumption for lot size cluster i and the constant a in Equation (1). Applying Equation (2) as an auto-regression equation for the data set in Figure 7 and adjusting α value to maximise the R2 value, the parameters obtained are listed in Table 1 (opposite). The Qi values in the table are plotted against the average lot size as shown by the blue diamond points in Figure 9. Applying a similar process used for selecting the indoor demand function, the logarithmic function is found to have the best fit. Although the Qi values include the constant a , which is less than --1.99 (because outdoor consumption for lot size less than 200m2 has to be greater than or equal to zero), the outdoor demand function should be a logarithmic function as QOutdoor = b+cln(L) (3) where b and c are constants. L is the lot size of a house. Finally the total consumption of a residential house can be expressed as Q = a+b+cln(L)+kHα (4) Unfortunately a and b values cannot be solved independently for cross-sectional data due to multi-colinearity. So a + b will be solved as a single parameter. However, they can be solved separately when Equation (4) includes seasonality and weather conditions. This will be discussed further in the next section. Applications Track indoor and outdoor savings over time The first application is to run the regression model (Equation (4)) on the WaterFix properties for each financial year from 2001-- 2002 to 2008--2009. For each financial year, property samples were chosen to satisfy the following conditions: • Participating in WaterFix program only • Owner occupied • Not sold during the modelling period • No swimming pool • Not a Department of Housing (DoH) property • The property exists for whole year • No check meters and/or related properties connecting to it. The estimated parameter values and indoor and outdoor savings due to drought restrictions over time are shown in Table 2 (overleaf). A constant α value of 0.72 was applied. Sensitivity analysis with a range of a values from 0.68 to 0.78 shows little effect on R2 value and final results. The indoor and outdoor savings were estimated as the difference in consumption between year 2001--2002 and the year estimated based on a typical house with a family of three people and a lot size of 500m2. The key assumption made is that a remains constant over time, so it would disappear in the saving estimation. For example, the indoor savings for year 2002--2003 can be calculated using Equation (5a) and (5b) (overleaf). 50 100 150 200 250 300 350 400 450 500 1234567 Household Size Average Consumption (kL/Yr) <=200 m2 201-400 m2 401-600 m2 601-800 m2 >800 m2 Figure 6: Consumption against household size during 2001--2002. 50 100 150 200 250 300 350 400 450 500 1234567 Household Size Average Consumption (kL/Yr) >=200 m2 201-400 m2 401-600 m2 601-800 m2 >800 m2 Figure 7: Consumption against household size during 2005--2006. Figure 9: Relation between outdoor consumption and lot size. y = 25.946Ln(x) - 131.72 R2 = 0.9883 -10 0 10 20 30 40 50 60 100 200 300 400 500 600 700 800 900 1,000 1,100 1,200 Lot Size (m 2) Consumption (kL/Yr) y = 75.274x0.7439 R2 = 0.9996 0 50 100 150 200 250 300 350 400 450 500 1234567 Household Size Average Consumption (kL/Yr) 401-600 m2 Figure 8: Relation between indoor consumption and household size.
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